In curved spacetimes, the case is indeed more difficult than that of the p-wave superconductor. In particular, covariantising the Fierz-Pauli equation and introducing \(U(1)\)  minimal couplings does not suffice to produce the required number of independent constraint equations [1]}. Consequently, spurious propagating degrees of freedom are left in the theory that lead to, in principle, disastrous inconsistencies such as the emergence of ghosts or the loss of hyperbolicity.
